The remaining pair, accused of supporting Osama Bin Laden’s bomb attacks on US embassies in Africa in 1998, said new evidence showed they had no links to the campaign.

They made the fresh applications to stay extradition after the European Court of Human Rights rejected their appeal bid, and in some cases they have been fighting being sent to the US for trial for more than 10 years.

This is the plane waiting to take radical cleric Abu Hamza and four other terrorist suspects back to the US after the high court cleared the way for their immediate extradition (GEOFF ROBINSON)

But Sir John Thomas, President of the Queen's Bench Division, and Mr Justice Ouseley, dismissed their claims in a judgment delivered on Friday afternoon.

It means Hamza and the other suspects should be flown to the US to face trial within a few days.

During the hearing earlier this week, counsel for the Home Secretary confirmed she would be “entitled to move instantly” if the appeal was rejected.

It will bring to an end a drawn-out saga that had provoked the concern of the most senior judge in England and Wales, the Lord Chief Justice.

The judges said they were "wholly unconvinced" that Hamza was unfit to plead, and the sooner he was put on trial the better it would be.

"We considered first the arguments on the basis that it was an application to re-open the appeal and therefore we should consider whether it would be unjust and oppressive to extradite him.

"We were wholly unpersuaded that on the evidence that he was unfit to plead. We concluded that if Abu Hamza might be unfit to plead, because of sleep deprivation and physical conditions at HMP Belmarsh, then this condition being treatable could be treated in the United States.

"If any potential unfitness to plead was emerging from a degenerative condition of the brain, the Court concluded that the sooner he is put on trial the better.

"In either case therefore there is nothing to suggest that extradition in this case would be unjust or oppressive.

"In light of this, we also found that there had been no material or significant change in circumstance of the kind to render it unlawful, or in breach of Convention rights, for Abu Hamza to be extradited."

The judges also pointed out that the suspects had "long ago exhausted" all the avenues available in Britain to avoid extradition, and having also gone to Strasbourg they have tried "every single point".

They said it was "unacceptable" and "not just" that extradition should have dragged on for eight and 14 years, with the process "disfigured" by the succession of appeals.

The senior judges raised the prospect of changes to the appeal process because of the "real dangers" in the system that allow old points to be raised again.

Shortly after the judgment, the Home Office said: "We welcome the High Court decision on Abu Hamza and others. We are now working to extradite these men as quickly as possible."

All five cases returned to the High Court after judges at the European Court of Human Rights refused to intervene and stop the Home Secretary extraditing them.

Between 1999 and 2006, the men were indicted on various terrorism charges in America.

Hamza has been charged with 11 counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001, and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.

Ahmad, a computer expert from south London, and Ahsan are accused of offences including using a website to provide support to terrorists and conspiracy to kill, kidnap, maim or injure persons or damage property in a foreign country.

They wanted their removal stopped so that they could challenge a decision by the Director of Public Prosecutions not to allow British businessman Karl Watkin, a campaigner against the UK's extradition arrangements with the United States, to bring prosecutions against them in the UK.

Bary and Al-Fawwaz were indicted - with Osama bin Laden and 20 others - for their alleged involvement in, or support for, the bombing of US embassies in Nairobi and Dar es Salaam in 1998.